AINS land surveyor system with reprocessing, AINS-LSSRP

ABSTRACT

A Land Surveyor System with Reprocessing is carried by a surveyor moving from a first known position at the start of a survey interval to a second known position at the end of the survey interval has an AINS (aided inertial navigation system) that provides a continuing sequence of time-indexed present position values. A Position Computing System uses a program that stores the sequence of time-indexed present position values in a memory. A reprocessing computer and program is activated at the second known position to access and process the continuing sequence of time-indexed present position values with a smoothing program to provide indexed and adjusted present position values for at least some of the time-indexed present position values. The system is packaged for transport and use by a surveyor. A switch permits the surveyor to signal that the unit is stationary as a reset for the AINS.

This non-provisional application claims priority from U.S. provisionalapplication Ser. No. 60/252,862 filed Nov. 22, 2000.

1. FIELD OF THE INVENTION

The subject invention relates to inertial navigation, and moreparticularly to aided inertial navigation systems (AINS) based LandSurveyor Systems which use an AINS as a navigational reference and whichmake it possible to survey forested areas where GPS signals may bemissing for long intervals of time or indefinitely due to foliage and ora dense tree canopy. Land surveyor systems that are not aided with aradio positioning system such as GPS as a result of signal blockage dueto a tree canopy tend to accumulate position error linearly as afunction of time.

2. BACKGROUND OF THE INVENTION

AINS technology originated in the late 1960′s and found application onmilitary navigation systems. An example or the many books on the subjectis the text by George Siouris, titled “Aerospace Avionics Systems, AModern Synthesis”, published by Academic Press, published in 1993.

Traditional methods of surveying used laser theodolites, which requiredaccess to lines of sight between positions to be surveyed. A line ofsight is not always available in forested areas. A line of sight wastypically obtained in the past by bulldozing corridors 3-4 meters widethrough the forest along the lines or paths to be surveyed. Governmentsdiscourage this wasteful and environmentally destructive practice byimposing stumpage fees on destroyed trees and other forms of penaltiesfor environmental damage. The advent of a precise GPS has provided analternative method of land surveying; however, a Land Survey Systembased exclusively on a precise GPS receiver is limited to areas wherethe sky is visible. Some tropical rain forests have canopies that are sodense that precise GPS cannot be used at all.

AINS Land Surveyor

An AINS land surveyor does not require access to the sky and can beoperated under a dense tree canopy. A single surveyor using an INS landsurveyor can map a forest or jungle area by walking a path among thetrees thereby avoiding the need to cut trees to establish a survey laneas would be required using theodolites or a precise GPS. Use of an AINSland surveyor therefore results in reduced cost, and the environmentalimpact of the survey is substantially reduced.

To reduce drift and obtain acceptable accuracy, the surveyor using anAINS-based land surveyor systems brings the INS to a complete rest aboutevery 1-2 minutes for a period of 5-30 seconds. This is called azero-velocity update (ZUPD). A Kalman filter uses each ZUPD to zero theINS velocity error and partially calibrate out inertial sensor errors.The position error drift with periodic ZUPD's is on the order of 0.5-2meters per kilometer, depending on the quality of the inertial sensorsand on the frequency of ZUPD's. The requirement for ZUPD's is often aninconvenience, since it limits the surveyor's production.

The Kalman filter in an AINS based Land Surveyor System is also coupledto receive measurement inputs from one or more external and independentsources which are processed to further refine or aid the navigationsolution. Aiding information can include aiding signals from sourcessuch as a precise GPS receiver, a Doppler Radar, or from an odometer ora precise pedometer. In the survey of an area permitting an unobstructedview of the sky, a precise GPS provides the simplest aiding signal.Several different accuracy levels are associated with GPS performanceand signals. C/A GPS implies uncorrected GPS, and provides 10-20 meter3D position accuracy. A GPS can be coupled via a radio modem link to abase GPS receiver, which has a precisely known position. The base GPSmeasures the errors in the signals being received and forwardscorrections via the model to the precise GPS aboard the navigator. AnRTCM-corrected differential GPS uses industry standard RTCM differentialcorrections from a dedicated base receiver or a differential correctionsservice such as the U.S. Coast Guard or Omnistar to obtain 0.5-1.0meters position accuracy. Real-time kinematic (RTK) GPS usesdifferential GPS data from a dedicated base receiver to obtain 0.05-0.1meters position accuracy.

The invention system allows a surveyor to carry the invention AINS-basedLand Surveyor System with Reprocessing along a predetermined path orline and to locate and record the position of stakes that the surveyorpositions in accordance with a pre-planned grid of locations. The stakesidentify the locations of sensors and explosive charges that are used ina seismic survey. The predetermined path begins and ends at position fix(PF) locations that are precisely known. The invention AINS-based LandSurveyor System with Reprocessing then uses the known PF locations ateach end of the path and a smoother algorithm to reprocess the stakelocations.

Seismic Exploration

Seismic exploration has as its object, the production of amulti-dimensional map of the geological structure over an area below theground for the purpose of identifying valuable oil, gas and mineraldeposits. A seismic survey uses acoustic interferometry to perform themulti-dimensional subterranean mapping. A geophysicist provides apre-plot map with grid locations of the desired positions of the noisesources and the geophones over the space to be explored. The noisesources are multiple phased dynamite explosions on a 2-dimensional gridpattern. The sound waves from the charges are reflected by the differentgeological strata, and received by an array of geophones on a separate2-dimensional grid connected to recording devices.

The multi-dimensional geological map is generated by post-processing therecorded data. The typical error specification for the position of anoise source or a geophone is one meter horizontal and 0.5 metersvertical.

A backpack-borne AINS based system is made and sold by the assignee ofthis application, Applanix Corporation. at 85 Leek Cresent, RichmondHill, Ontario, Canada L4B 3B3. The system is called the Position andOrientation System for Land Survey (POS/LS). In operation, a surveyorwalks a survey path or trajectory carrying the POS/LS as a backpack.Such survey trajectories often pass through areas where GPS signals arenot available. The POS/LS navigates though such GPS outage areas in adead-reckoning mode with as little position drift as possible. Typicallythe surveyor moves from one known position to another, and “ties-down”or “fixes” the POS/LS position at the known positions.

The path followed by a surveyor is typically a zigzag pattern ofparallel seismic lines, each 1000-5000 meters long with the stakespositioned every 50-200 meters on the lines. A control survey issometimes performed to verify the accuracy of the seismic survey. Acontrol survey is formed by a number of short survey paths between knownpositions with traverse legs being approximately perpendicular to theprincipal seismic or grid lines. Intersections of the control paths withthe seismic lines form the control points. The control point positionaccuracies should be significantly better than the seismic line positionaccuracies.

SUMMARY OF THE INVENTION

This invention teaches the use of an optimal smoothing algorithm and amethod of reprocessing the data accumulated and stored from an AINS-LandSurveyor System with Reprocessing (AINS-LSSRP) between known positionfixes or “tie-downs”.

A first embodiment of the AINS-LSSRP comprises an AINS that provides asequence time-indexed present position values in response to the LSSRPbeing moved from a first known position value or PF at the start of asurvey interval to a second known position value at the end of thesurvey interval. The LSSRP has a Position and Orientation (POS) ComputerSubsystem (PCS) coupled to receive and store the sequence oftime-indexed present position values as the surveyor moves from thefirst known position to the second known position. The PCS has areprocessing computer and program means for processing the indexedpresent position values with a smoothing algorithm to provide indexedand adjusted present position values for at least some of the indexedpresent position values recorded as the LSSRP was moved from and betweenthe first known position value at the start of the survey interval andthe second known position value at the end of the survey interval.

In a more particular alternative embodiment, of the LSSRP, the AINS usesa Kalman filter responsive to at least two sources of aiding signals,and the PCS has an aiding signal selector algorithm characterized toselect the most accurate aiding signal for use by the Kalman filter fromall available aiding signals.

In yet another more particular embodiment of the LSSRP, the AINS uses areprocessing computer and program means smoothing algorithm that is usedis a Modified Bryson-Frazier smoother (MBFS).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an aided INS system;

FIG. 2 is a block diagram of the Aided Inertial Navigation System-LandSurveyor System with Reprocessing (AINS-LSSRP);

FIG. 3 is a schematic characterization showing a top graph of real-timeposition error growing linearly with time; a lower graph showsreprocessed position solutions with a maximum average error at alocation approximately between position fixes;

FIG. 4a is a graph of real-time position error, the system using ZUPD'seach minute to aid the AINS between position fixes;

FIG. 4b is a graph of real-time position error, the system using ZUPD'seach minute to aid the AINS between position fixes, the positions beingreprocessed;

FIG. 5 is a flow chart for a computer program for storing time positionvalues as the system moves between position fixes and for reprocessingthe real-time position values at the end of a position fix;

FIG. 6 is a flow chart for signaling the start of recording smootherdata at the beginning of a survey interval and for subsequently closingthe smoother data file at the end of the survey interval; and

FIG. 7 is a flow chart for signaling the start of running the smootherfilter at the end of the previous survey interval.

DETAILED DESCRIPTION OF THE INVENTION

The invention taught herein improves the accuracy of reported stakepositions by combining the benefits of an AINS, such as the AINS used inan Applanix Position and Orientation System for Land Survey (POS/LS)with the steps of onboard data reprocessing. The combination forms anAINS-Land Surveyor System with Reprocessing (AINS-LSSRP) represented byblock 42 in FIG. 2. In operation and use, a surveyor begins a surveyinterval or leg from a position fix (PF) location having a preciselyknown location. The surveyor initializes the present position of hisAINS-LSSRP using differential GPS or a pre-surveyed marker. The surveyorthen follows predetermined survey lines or paths that run for severalkilometers in accordance with desired grid locations on a map. Thesurveyor may follow a zigzag pattern where the survey lines go into treecovered areas and where GPS contact is sometimes lost. In some rainforests, such as those in Indonesia, GPS can be lost for an entire day.The surveyor uses the AINS-LSSRP to position stakes at the predeterminedgrid locations and on reaching a second PF, the surveyor resets or “tiesdown” the AINS-LSSRP position with the precise position coordinates ofthe PF. The AINS-LSSRP then launches the reprocessing function, whichreprocesses and adjusts data gathered in the course of the traversebetween the two PF locations including the recorded positions of thestakes using a smoothing algorithm. The adjusted positions of the stakesare reported as a product of the survey.

FIG. 1 shows a generic Aided INS architecture. The elements withinphantom box 20 represent an inertial navigation system (INS), having aninertial measurement unit (IMU) 22 and an inertial navigator 24. Theinertial navigator is typically mechanized using a digital computer andsoftware for processing signals from and for delivering signals to theIMU 22.

The IMU 22 comprises a triad of accelerometers (not shown) that measuretotal specific force to restore a proof mass, the force beingproportional to acceleration, and a triad of gyros (not shown) thatmeasure total angular rate. The IMU also provides the supporting processand interface electronics (also not shown) that convert and output theinertial acceleration and angular rate signal data in a digital format.The inertial navigator is a mechanization of Newton's equations ofmotion, in software, typically running on the aforementioned digitalcomputer. To do this, the INS 20 typically aligns or transforms thesignal data from its package or vehicle navigation coordinate frame intoa fixed and earth referenced coordinate system, such as a North, Eastand Down directions. In some mechanization's, the horizontal axes isaligned to a heading other than North/East and the heading offset angleis called the wander angle. A typical ground alignment requires the INSto be stationary for 5-15 minutes so that the INS can measure thegravity vector with its accelerometers to establish Down alignment andwith a knowledge of the latitude, measure the horizontal component ofthe earth rotational rate vector with its gyros to establish the Northdirection and or the wander angle.

An aided inertial navigation system (AINS) 26 typically comprises an INS20, one or more aiding sensors such as the GPS receivers 28, a DopplerRadar 30 or a distance measuring instrument (DMI). A Kalman filter 34and a mechanism such as the error controller 35 process corrections tothe INS 20.

Notation

The following notation is used in this description of the invention.Lower case letters denote vectors. For example, {right arrow over (x)}denotes a vector. Upper case letters denote matrices. For example, Hdenotes a matrix.

Subscripts on vectors and matrices are used to indicate a discretesequence number that correspond to a sample time. For example, thematrix H_(k) denotes that the time of validity of the matrix H is sampletime t_(k), and hence is the k-th sample in a discrete time series of H.

“E” denotes the expectation operator. See A. Papoulis, “Probability,Random Variables and Stochastic Processes”, McGraw-Hill, 1965 or anyother reference on random variables for its definition.

Kalman Filter

The Kalman filter 34 is a recursive minimum-variance estimationalgorithm that computes an estimate of a state vector based onconstructed measurements. The measurements typically comprise computeddifferences between the inertial navigation solution elements andcorresponding data elements from the aiding sensors. For example, aninertial-GPS position measurement comprises the differences in thelatitudes, longitudes and altitudes respectively computed by theinertial navigator and a GPS receiver. The true positions cancel in thedifferences, so that the differences in the position errors remain. AKalman filter designed for integration in an INS with aiding sensorsestimates the errors in the INS outputs and aiding sensors. INS errorstypically include: inertial North, East and Down position errors;inertial North; East and Down velocity errors; inertial platformmisalignment in the local level vector and wander angle errors;accelerometer biases and gyro biases. Aiding sensor errors can includethe following: GPS North, East and Down position errors; GPS carrierphase ambiguities and DMI scale factor error.

The Kalman filter therefore performs as an optimal linear minimumvariance estimator that operates on a time series of measurements toestimate the state vector of a linear stochastic multivariable model ofthe form:

{right arrow over (x)} _(k+1)=Φ(k+1:k){right arrow over (x)} _(k)+{rightarrow over (μ)}_(k)

{right arrow over (z)} _(k) =H _(k) {right arrow over (x)} _(k)+{rightarrow over (η)}_(k)  (1)

where

{right arrow over (x)}_(k) is the n-dimensioned state vector at discretetime t_(k),

Φ(k+1;k) is called the transition matrix, or the n×n system dynamicsstate transition matrix. It is the discrete version of the system matrixΦ and is analogous to the F matrix that appears in the text by G.Siouris referenced above.

{right arrow over (μ)}_(k) is an n-dimensioned vector of process noiseswith variance Q_(k) where

E[{right arrow over (μ)} _(k){right arrow over (μ)}_(k+j)^(T)]=Q_(k)δ_(j)  (2)

The subscripts k and k+j are sample counts or indices. The samples arevalid at discrete times t of k) and t of (k+j). The dependency on time tis dropped and only the sample indices of k and j are retained toidentify the discrete samples.

The {right arrow over (μ)}_(k) symbol is a way of specifying whitenoise. Equation (2) above represents the expected value of a noisevector at one time multiplied by the noise vector transpose at asubsequent time, the product being equal to the covariance matrix Qtimes the delta function which basically says that the expected value isnon-zero only when the two times are the same. In other words, noisevectors sampled at different times are completely uncorrelated. Thearrow above μ_(k) indicates that it is an n-dimensional vector ofprocess noises with variance. The process noise is not a known error.Process noise is the driving noise in the stochastic model for thedynamics that the Kalman filter is designed to estimate. The statevector is therefore a vector of random variables whose randomnessrequires the use of a Kalman filter.

If a process has no noise, then it should be possible to predict everyfuture value of that process based on some initial value. If the firstvalue is known and the system dynamics state transition matrix is Φ(Phi) that describes how that process proceeds, then in the absence ofnoise, every future value can be predicted exactly. A Kalman filter isnot necessary in such systems.

{right arrow over (z)}_(k) is the m-dimensioned measurement vector atdiscrete time t_(k). In operation, it is equal to a position fix atdiscrete time t_(k).

H_(k) is the m×n measurement model matrix, or measurement matrix.

{right arrow over (η)}_(k) is the m-dimensioned vector of measurementnoises with variance:

E[{right arrow over (η)} _(k){right arrow over (η)}_(k+τ) ^(T) ]=R_(k)δ_(τ)  (3)

As above, terms that begin with “E[ ]” imply an expected or averagevalue.

where δ_(k) is the discrete delta function given by:

δ_(k)=1 when k=0,δ_(k)=0 otherwise.

Φ(k+1;k) describes the transition of the dynamic system from sample k attime t_(k) to sample k+1 at time t_(k+1). A text by T. Kailath, “LinearSystems”, Prentis-Hall, Inc. 19 100 provides a further discussion. Sucha model is often used to model the behavior of a noisy multivariableprocess. A Kalman filter is used to estimate the internal dynamicparameters of the process based on noisy measurements of the process.This is the conventional method of modeling and estimating the errors ofan INS system such as that shown in FIG. 1. The Kalman filter isconstrained to causal operation, hence its estimate of a state vector isthe optimal estimate based on all past and current measurements. Thefollowing equations describe the standard Kalman filter:

Extrapolation or Time Update

Equations 4 and 5 below extrapolate the state vector {right arrow over(x)}_(k) from sample time t_(k−1) to sample time t_(k). The state vector{right arrow over (x)}_(k) is updated at sample time t_(k) usingmeasurements valid at time k and again for the next sample time t_(k+1).

{right arrow over({circumflex over (x)})} _(k) ⁻=Φ(k:k−1){right arrowover({circumflex over (x)})} _(k−1) ⁻  (4)

P _(k) ⁻=Φ(k:k−1)P _(k−1) ⁺Φ(k:k−1)^(T) +Q _(k−1)  (5)

Equations 4 and 5 show that the transition matrix Φ transitions thestate estimate of the state vector {right arrow over (x)}_(k) fromsample k−1 to sample k. The transition matrix Φ(k; k−1) describes thesystem dynamics in a discrete setting.

Measurement Update

{right arrow over({circumflex over (x)})} _(k) ⁺ ={right arrowover({circumflex over (x)})} _(k) ⁻ +K _(k){right arrow over(ξ)}_(k)  (6)

{right arrow over (ξ)}_(k) ={right arrow over (z)} _(k) −H _(k) {rightarrow over (x)} _(k) ⁻  (7)

P _(k) ⁺=(I−K _(k) H _(k))P _(k) ⁻  (8)

K _(k) =P _(k) ⁻ H _(k) ^(T) S _(k) ⁻¹  (9)

S _(k) =H _(k) P _(k) ⁻ H _(k) ^(T) +R _(k)  (10)

where

{right arrow over({circumflex over (x)})}_(k) ⁻ is the priori (beforemeasurement update) estimate of the state vector,

{right arrow over({circumflex over (x)})}_(k) ⁺ is the posteriori (aftermeasurement update) estimate of the state vector,

{right arrow over (ξ)}_(k) is the Equations 4 and 5 innovations vector.The term “innovations” is an established and accepted term in Kalmanfiltering that describes the difference between the measurement vector{right arrow over (z)}_(k) and the model for the measurement vectorH_(k) before the update is processed.

P_(k) ⁻ is the priori estimation error variance-covariance (VCV) matrix,

P_(k) ⁺ is the posteriori estimation VCV matrix,

K_(k) is the Kalman gain matrix,

S_(k) is the innovations VCV matrix.

The VCV matrices P_(k) ⁻, P_(k) ⁺ and S_(k) are propagated in parallelwith the state vector {right arrow over({circumflex over (x)})}_(k)^(+/−) using equations (5) and (8). The discrete system dynamics aredefined per equation (1). The VCV matrix is then propagated.

The estimation error VCV matrix describes the Kalman filter's predictedestimation error propagation statistics as follows:

P _(k) ^(+/−) ≈E[({right arrow over (x)} _(k) ^(+/−) −{right arrow over(x)} _(k))({right arrow over (x)} _(k) ^(+/−) −{right arrow over (x)}_(k))^(T)]  (11)

The diagonal elements of equation (11) are the predicted estimationerror variances for the individual state vector elements. If the modelof equation (1) exactly describes the system dynamics and measurements,then the estimation error VCV matrix exactly describes the estimationerror statistics of equation (11). The model of equation (1) is at bestan approximation for a nonlinear system; therefore the estimation errorVCV matrix is interpreted for each case.

The minus and plus exponents in the above equations imply valuesrespectively occurring before and after the Kalman filter measurementupdate at a given time index k. A (−) superscript indicate a beforemeasurement update. A (+) superscript indicates an after measurementupdate. A (+/−) indicates that the equation holds for either case. Thisnotation is used in a related text titled “Applied Optimal Estimation”,MIT Press 1994 (12th printing 19 112) by A. Gelb, (editor).

The theoretical value of the covariance matrix is the expected value ofthe error vector times the error vector transpose. The product of twoparameters is the cross correlation or the autocorrelation between thosetwo values. If they are uncorrelated from one sample to the next thenthe autocorrelation is zero except at the time when the two samples arevalid or at a point where the two samples are taken at the same time.They are equal to the variance if it is a scalar or to the covariance ifit is a vector.

At the conclusion of each AINS system navigational solution, a timeblended position is the result. If the Kalman filter is designed tointerface to a smoother, it writes the following variables to a filewhich the smoother later reads:

Φ(k+1;k) transition matrix from k to k+1

H_(k) measurement matrix at iteration k

K_(k) Kalman gain at iteration k

S_(k) Kalman innovations covariance at iteration k

innovations vector at iteration k. See page 317 in Gelb's “AppliedOptimal Estimation” text referenced below.

Kalman estimated error state at iteration k

Kalman generated estimation error VCV matrix at iteration k

To implement a Kalman filter, the designer first chooses or codes theparameters Φ(k+1;k), Q_(k), H_(k) and R_(k) so that the Kalman filterproperly models the process being estimated. If the process beingestimated is the INS error process, then the parameters Φ(k+1;k) andQ_(k) are derived from one of several known INS error models. Errormodels are discussed in the above referenced text by George Siouris,titled “Aerospace Avionics Systems, A Modem Synthesis”, published byAcademic Press, published in 1993. The designer then designs themeasurements {overscore (z)}_(k) that the Kalman filter will process,and from these measurements, the filter computes and implements themeasurement model parameters H_(k) and R_(k). For a GPS-aided INS, themeasurements {overscore (z)}_(k) are typically differences between theINS and GPS position and velocity data. H_(k) describes the measurementgeometry with respect to the state vector {right arrow over (x)}_(k),and R_(k) describes the measurement noise variance or relative weightingof each scalar measurement in the measurement vector {overscore(z)}_(k). The steps in Kalman filter design are discussed in severaltexts, one of which is mentioned above, i.e., the text by A. Gelb titled“Applied Optimal Estimation”, MIT Press 1994 (12th printing 19 112) by,(editor).

Equations 4 through 10 above describe the full mechanization of theKalman filter, given the above model parameters and measurements. Thereare also several references on numerically stable and efficientimplementations of these equations. A popular implementation is thatdisclosed as the Bierman implementation described in the text titled“Factorization Methods For Discrete Sequential Estimation” by G. J.Bierman and published by Academic Press in 1977.

Optimal Smoothing Algorithms and Methods

A smoothing algorithm is defined here to be any algorithm that computesan estimate of a quantity or collection of quantities assembled into avector at a given estimation time using measured data having times ofvalidity before and after the estimation time.

An optimal fixed interval smoother computes the optimal estimate basedon all past, current and some future measurements. It is characterizedin the text by A. Gelb, referenced above, as a varianceweighted—weighted combination of a Kalman filter running forward in timeon a data time series and a Kalman filter running backward in time onthe same data time series. The fixed interval smoother operates on allavailable measurements to compute the optimal estimate at each sampletime based on all measurements during a defined process interval.

Different smoother formulations can be obtained by the algebraicmanipulation of the basic forward-backward Kalman filter smoother. Thefollowing equations describe one such formulation that is developedfurther in the text title “Applied Optimal Control” by A. E. Bryson Jr.and Y. C. Ho, published by Wiley and Sons, 1975. The smoother isreferred to as the modified Bryson-Frazier smoother (MBFS).

Backwards Extrapolation

{right arrow over (λ)}_(k−1) ⁺=Φ^(T)(k:k−1){right arrow over (λ)}_(k)⁻  (12)

Λ_(k−1) ⁺=Φ^(T)(k:k−1)Λ_(k) ⁻Φ(k:k−1)  (13)

Adjoint Measurement Update

{right arrow over (λ)}_(k) ⁻=(I−H _(k) K _(k)){right arrow over (λ)}_(k)⁺ −H _(k) S _(k) ⁻¹{right arrow over (ξ)}_(k)  (14)

Λ_(k) ⁻=(I−H _(k) K _(k))^(T)Λ_(k) ⁺(I−H _(k) K _(k))+H _(k) ^(T) S _(k)H _(k)  (15)

where:

{right arrow over (Λ)}_(k) ⁻ is the a priori adjoint state vector,

Λ_(k) ⁻ is the a priori adjoint VCV matrix,

{right arrow over (Λ)}_(k) ⁺ is the a posteriori state vector, and

Λ_(k) ⁺ is the a posteriori adjoint VCV matrix.

The input data to the MBFS at the k-th iteration of the MBFS comprisesthe following data items that a Kalman filter designed for interface toa MBFS computes internally and writes to data files:

Φ(k;k−1) transition matrix from iteration k−1 to iteration k

H_(k) measurement matrix at iteration k

K_(k) Kalman gain at iteration k

S_(k) Kalman innovations covariance at iteration k

{right arrow over (ξ)}_(k) innovations vector at iteration k. See page317 in Gelb's “Applied Optimal Estimation” text referenced above.

{right arrow over({circumflex over (x)})}_(k) ⁺ Kalman estimated errorstate at iteration k

P_(k) ⁺ Kalman generated estimation error VCV matrix at iteration k

The smoothed state and estimation error VCV matrix are obtained asfollows:

{right arrow over (x)} _(k) ^(s) ={right arrow over (x)} _(k) ⁻ −P _(k)³¹{right arrow over (λ)}_(k) ⁻ ={right arrow over (x)} _(k) ⁺ −P _(k)⁺{right arrow over (λ)}_(k) ⁺  (16)

P _(k) ^(s) =P _(k) ⁻(I−Λ _(k) ⁻ P _(k) ⁻)=P _(k) ⁺(I−Λ _(k) ⁺ P _(k)⁺)  (17)

Note that smoothing with the a priori or a posteriori states and VCVmatrices yields the same smoothed state and VCV matrix. This is themathematical expression of the fact that the smoothed estimate at anyestimation time is the optimal estimate based on all measurements,before and after the estimation time.

Application of Optimal Smoothing to the AINS-LSSRP

A smoother designed for an AINS-LSSRP comprises two components: thesmoothed estimation operation and the position solution correctionoperation.

The smoothed estimation operation uses the MBFS described previouslythat is made specific to the AINS component of the AINS-LSSRP primarilythrough the design of the stochastic state and measurement models inEquation 1. The Kalman filter is designed to estimate the errors in theINS and siding sensors. This a well-understood practice among navigationpractitioners, and is described in G. Siouris referenced above andreviewed here briefly.

The elements of the state vector {right arrow over (x)}_(k) in Equation1 comprise the INS navigation errors (position, velocity and attitudeerrors), inertial sensor errors (accelerometer and gyro biases andpossibly other errors) and aiding sensor errors. The AINS-LSSRP requiresan improved position solution only, hence the state vector is given thefollowing representation: $\begin{matrix}{{\overset{\rightharpoonup}{x}}_{k} = \begin{bmatrix}{\delta \quad \overset{\rightharpoonup}{r}} \\{\overset{\rightharpoonup}{x}}_{remaining}\end{bmatrix}} & (18)\end{matrix}$

where

δ{right arrow over (r)} is the AINS position error

{right arrow over (x)}_(remaining) is the sub-vector of error statesother than δ{right arrow over (r)}

The elements of the measurement vector {right arrow over (z)}_(k) inEquation 1 comprise differences between the positions and velocitiescomputed by the INS and corresponding positions and velocities from theaiding sensors. The Kalman filter thus compares components of the INSnavigation solution with corresponding components from the aidingsensors, and thereby estimates the errors in the INS navigation solutionand the aiding sensors.

The AINS then corrects the INS navigation algorithm with the estimatedINS navigation errors. The closed-loop between the INS and the AINSKalman filter shown in FIG. 1 achieves regulation of the INS errors toconsistency with the aiding sensor errors. If the adding sensors includea GPS receiver, then the AINS navigation errors will be consistent withthe GPS navigation errors. In particular, AINS error regulationsuppresses the INS position error drift, and the Kalman filter estimatesand thereby calibrates the inertial sensor errors such as theaccelerometer and gyro biases. By using a Kalman filter to estimate theINS errors, the AINS achieves a theoretically optimal (in theleast-squares sense) navigation error based on all past and currentaiding sensor data.

The MBFS described in Equations 12 to 15 operates on data generated bythe AINS Kalman filter and written to data files, and computes asmoothed error state and VCV described in Equations 16 and 17 that haveimproved accuracy over the estimated error state from the AINS Kalmanfilter. The improvement results from the fact that the MBFS computes theoptimal estimate (in the least-squares sense) at an iteration k based onall aiding sensor data before and after the iteration k. The MBFS thuscomputes estimates of the INS position, velocity and attitude errors,called the smoothed INS errors, that the AINS error regulation mechanismwas unable to correct because of the causal constraint on access toaiding sensor data. The smoothed error state is partitioned as followscompatible with Equation 18. $\begin{matrix}{{\overset{\rightharpoonup}{x}}_{k}^{s} = \begin{bmatrix}{\delta \quad {\overset{\rightharpoonup}{r}}_{s}} \\{\overset{\rightharpoonup}{x}}_{remaining}^{s}\end{bmatrix}} & (19)\end{matrix}$

where

δ{right arrow over (r)}_(s) is the smoothed estimate of AINS positionerror

{right arrow over (x)}_(remaining) ^(s) is the sub-vector of smoothederror states other than δ{right arrow over (r)}_(s)

The position solution correction operation corrects the AINS positionsolution by simple subtraction of the smoothed AINS position errors fromthe AINS position solution. The actual mechanization depends on the AINSposition coordinate format, which can be one selected from the followingpossible formats: geographic (latitude, longitude, altitude), UniversalTransverse Mercatur (UTM) (Northing, Easting, height) or earth-fixedCartesian (X, Y, Z components of position vector {right arrow over(r)}_(k) ^(e)). The following example corrects an earth-fixed Cartesianposition vector {right arrow over (r)}_(k) ^(e) to obtain the correctedor reprocessed position vector {right arrow over (r)}_(s) _(k) ^(e).$\begin{matrix}{{\overset{\rightharpoonup}{r}}_{s_{k}}^{e} = {{{\overset{\rightharpoonup}{r}}_{k}^{e} - {\delta \quad {\overset{\rightharpoonup}{r}}_{s}}} = \begin{bmatrix}{{\hat{r}}_{x}^{e} - {\delta \quad {\hat{r}}_{s_{x}}^{e}}} \\{{\hat{r}}_{y}^{e} - {\delta \quad {\hat{r}}_{s_{y}}^{e}}} \\{{\hat{r}}_{z}^{e} - {\delta \quad {\hat{r}}_{s_{z}}^{e}}}\end{bmatrix}}} & (20)\end{matrix}$

Zero-Velocity Update (ZUPD)

The AINS-LSSRP represented by block 42 in FIG. 2 is brought to acomplete rest periodically, typically every 1-2 minutes, for a period of5-30 seconds. Each rest period is called a zero-velocity update (ZUPD).A Kalman integration filter uses these zero velocity observations tozero the INS velocity error and to null inertial sensor rate errors. AnAINS-LSSRP (Land Surveyor System with Reprocessing) can reduce positionerror drift with periodic ZUPD's to a value of 0.5-2 meters perkilometer depending on the quality of the inertial sensors and the timebetween ZUPD's. However, the requirement for ZUPD's limits thesurveyor's production.

Referring to FIG. 3, survey lines are called traverses. The surveyorstarts each traverse interval from a known position, referred to in FIG.3 as a PF interval, an indexed position fix at a mapped survey gridlocation. The surveyor then follows the survey lines while positioningstakes at required map grid locations. The surveyor continues along thetraverse and tries to end up at another known position and does a “tiedown” where he establishes the next PF or position fix. “Tying down”means that the surveyor arrives at the second known position and entersthe known coordinates of the position fix into this navigation system.The position error that has accumulated over the traverse is reset tozero.

The reprocessing feature of the invention activates the processor'ssmoother algorithm at each “tie-down”. Reprocessing enables the systemto use the recently stored data to calculate the errors and to correctthe position of stakes located in the course of the traverse intervalbetween position fixes. Having corrected the locations of the stakes fora completed traverse, the system is free to retain or delete thepreviously stored time-indexed position values if memory constraintsrequire the storage space used for the previously stored time-indexedposition values be made available for use in the course of the nextsurvey interval.

The time indexed solutions are position values that the AINS computesand logs in a mass memory unit as the surveyor is traversing a surveyline between position fixes. As a tie down location is reached, theoperator pushes a button or otherwise initiates the reprocessingfunction. In the alternative, the operator could transfer the knownposition values for the tie down as a pre-recorded waypoint, push thebutton and keep going. The computer can navigate with time navigation ona second traverse while running the smoother on the recorded positionsfrom a first traverse.

As the smoothing algorithm completes the smoothing process, it outputs asmoothed error table and surveyed positions with improved accuracy forthe data gathered in the previous traverse. The smoothed error table isa close estimate of the position error for each time position in theprevious traverse. Curve 58 in FIG. 3 schematically depicts there-processed position error from a completed survey interval.

FIG. 2 is a block diagram of an embodiment of the invention AINS-LSSRP42 that uses a generic smoothing algorithm to re-process the aidedinertial navigation data. The AINS-LSSRP 42 comprises an AINS 26 withaiding signal sources therein as shown in FIG. 1, a processing computercalled the POS computer subsystem (PCS) 44 comprising a STORAGE DEVICE46, a reprocessing computer and program means 45, and an aiding signalselector 43. Input/output interface device is coupled to the PCS 44 andallows the survey to input data into the AINS 26, reprocessing computerand program means 45 and aiding signal selector 43 as required.

Input/output interface device 48 is typically a keyboard and/or adisplay, with which the operator uses to initiate reprocessing at aknown tie-down or position fix. The interface device has a mode controlbus 36 coupled to the aiding signal selector input 51, a position fixentry bus 37 coupled to the AINS 26 from output 39 and an input/outputbus 38 coupled from output port 40 to the reprocessing computer andprogram means input 41. The mode control bus 36 and the input/output bus38 provide input and output control signals and position values andsmoothed position values as required between the respective functionalblocks for control, display and data transfer purposes.

The AINS 26 provides a series of real-time position values via bus 27 tothe reprocessing computer and program bus 45 for transfer and storage inarrays of memory locations in mass storage memory 46 via data bus 49.The time-indexed position values are output during each traverse between“tie-downs” via bus 27 to the reprocessing computer and program meansblock 45 and via data bus 49 to mass storage memory 46.

The reprocessing computer and program bus 45 reprocesses and filterseach set of time-indexed position values. The aiding signal selector 43is programmed or controlled by an input from the surveyor via theinput/output interface device 48 via bus 36 to direct the AINS 26 toselect the most accurate of the aiding signals available, such as aprecise GPS aiding position signal.

Input/output interface device 48 receives position values (PF values)from the surveyor and transfers the values to the AINS 26 and to thereprocessing computer and program means 45. The reprocessing computerand program bus 45 is programmed with the algorithm that mechanizes asmoother filter such as the filter characterized by equations 12 through17 above.

The aiding signal selector 43 is typically a computer program, asequential machine or software program, or an operator-controlledsoftware switch that selects the highest accuracy time-indexed aidingposition values available and couples the selected aiding signal valuesto the AINS 26 or directs the AINS 26 as to which signal source toselect. By way of example, if the radio modem drops out, the GPSposition accuracy can drop from 0.05 meters to 20 meters. If theAINS-LSSRP has maintained a position accuracy of better than a fewmeters, the aiding signal selector would direct the AINS to treat aradio modem link loss as a complete GPS outage. Alternatively theoperator may be suspicious of GPS accuracy and would then manuallydeselect GPS data processing by the AINS.

The AINS-LSSRP will not use C/A quality GPS data because it can achievebetter position accuracy between two position fixes using ZUPD aidingalone. In this mode, the AINS-LSSRP navigates as if GPS data is notavailable in the absence of a radio modem link. Re-processing isimportant in this case even though the receiver has clear access to GPSC/A quality signals from the GPS satellites. Since the radio modem canbe lost, without notice, at any time, ZUPD's continue to be necessaryfor improved accuracy.

FIG. 2 shows that aiding signal selector is coupled to AINS 26 viasignal path 25. It should be understood that all data might be coupledbetween the all of the blocks shown via a common bus connecting thefunctions characterized in FIG. 2. The reprocessing computer and programbus 45 reads the set of time-indexed position values and smoother valuesfrom the Kalman filter in INS 26 and uses the start position fix ortie-down and end position fix or tie-down and all of the time-indexedposition values from the previous related traverse to calculate anestimated error for each time-indexed position value or PF for eachtraverse. The error is then applied to correct each correspondingtime-indexed position value to provide a set of corrected or adjustedtime-indexed position fixes. Each filtered time-indexed position fix hasan accuracy that is improved over the accuracy of the correspondingtime-indexed position value fix.

In a more particular embodiment of the AINS-LSSRP 42, the reprocessingcomputer and program bus 45 for reprocessing and filtering a set oftime-indexed position values is programmed to be a smoother such as aModified Bryson-Frazier Smoother (MBFS) that operates on all availablemeasurement values to compute optimal estimates of position values basedon all measurements during a defined processing interval or traverse.The MBFS operates on a set of time-indexed position values for eachtraverse using the start PF and the end PF values with the positionvalues benefiting from all ZUPD's between the start and end positionfixes.

FIG. 3 schematically shows that the real-time position error, top curve54 increases linearly with time and reaches a maximum at peak 56 on thelast position solution before the AINS Kalman filter processes the nextposition fix. By contrast, curve 58 shows that the reprocessed positionsolution exhibits a maximum average error approximately midway betweenposition fixes. A survey interval therefore comprises a PF interval plusa subsequent traverse interval plus the next PF interval. A surveyinterval thus begins with the start of a PF interval and ends with theend of the subsequent PF interval.

FIG. 4a shows a plot of real-time radial position error data as afunction of time in thousands of seconds. FIG. 4b shows a plot of thereprocessed position error data as a function of time in thousands ofseconds. ZUPD's were used to aid the AINS between position fixes. Thereference position for computing the radial error was obtained from aprecision GPS position solution with 0.05 meter accuracy.

A Position Fix

A “position fix started” condition is determined when the operatordirects the AINS-LSSRP to perform a position fix/ZUPD at a pre-surveyedlocation. The system is stationary at the time; therefore, a positionfix is a combination of position fix and a ZUPD. The operator enters theposition coordinates using the input/output interface device 48,typically a handheld screen/keyboard.

As an alternative, a precise GPS calculated position may be transferredvia a link such as an infrared or optical, acoustic or electrical linkin place of an operator manually entered position to avoid errors andreduce the operator workload. As presently conceived, a manual actionfrom the operator initiates or triggers the transfer of a position fixfrom the GPS to the system at the location of a tie-down. As analternative embodiment, the GPS position is used in place of themanually entered position to avoid operator-induced errors.

Blocks 52-60 of FIG. 5 shows the steps performed by the generic AINS 26,described schematically in FIG. 1. The steps begin at ENTER block 52.The AINS 26 receives IMM data such as accelerations and rotation ratesvia block 54 at the IMU sampling rate, of typically 50-500 Hz andoccasionally as high as 1000 Hz. The inertial navigator algorithm 56,operates on the data, to update each IMU record and to provide atime-indexed INS navigation solution.

The decision 58 to run the Kalman filter can be based on time or onavailability of aiding values. If, for example, a GPS receiver nominallyprovides position information every 1 second, then AINS can run theKalman filter every 1 second with the arrival of each batch of new GPSdata. Alternatively, if only ZUPD's are available, the Kalman filter isrun at the completion of each respective ZUPD.

At the conclusion of each cycle, or indexed computation, the KalmanFilter, represented by block 34 in FIG. 1, and the RUN THE KALMAN FILTERAND CORRECT THE INERTIAL NAVIGATOR WITH ESTIMATED ERRORS (FIG. 1) block60 in FIG. 5, updates its estimate of the INS errors. The Kalman filterprovides its estimate to the error controller block 35, on FIG. 1, thatis used to send navigator correction signals to the Inertial Navigator24.

FIG. 5 shows the RUN THE DR FUNCTION FOR SURVEY INTERVAL [k, k+1] (FIG.6) block 90, and the RUN THE DR FUNCTION FOR SURVEY INTERVAL [k+1, k+2](FIG. 6) block 110. FIG. 5 also shows the RUN THE SEC FUNCTION FORSURVEY INTERVAL [k, k+1] (FIG. 7) block 130 and the RUN THE SEC FUNCTIONFOR SURVEY INTERVAL [k+1, k+2] (FIG. 7) block 150.

The DR and SEC Functions 90, 130 in FIG. 5 collectively describe thereprocessing function. The DR and SEC Functions run whenever theAINS-LSSRP Kalman filter 34 runs. The Kalman filter can process a singleposition fix measurement or a succession of measurements of the sameposition fix during a Position Fix (PF) interval during which theAINS-LSSRP is stationary at a known position. The Kalman filter willprocesses ZUPD measurements, precise pedometer or other aiding inputmeasurements but not position measurements during a traverse interval.The AINS-LSSRP position error will drift at a specified rate. Inprocessing a position fix during a PF interval after a traverseinterval, the Kalman filter updates its estimate of AINS position errorand reduces its position uncertainty from the accumulated position driftduring the traverse interval to the uncertainty in the position fix,typically one the order of a few centimeters to a few decimetersdepending on the accuracy of the surveyed position or of the precise GPSposition information available.

Two pairs of blocks 90, 130 and 110, 150 depict two successive PFintervals during which the Kalman filter processes a succession ofmeasurements of a position fix. The first time traverse interval isidentified as the [k, k+1] interval. The [k, k+1] interval starts whenthe AINS-LSSRP begins to be stationary at a known position and theKalman filter begins to process measurements every n-th second(typically every one second) of the known position. The Kalman filtermay also process other measurements such as ZUPD measurements orpedometer measurements if these are enabled as part of the AINS-LSSRP.The [k, k+1] interval ends when the AINS-LSSRP begins to move and theKalman filter stops processing position fix measurements. Interval [k,k+1] can describe a single Kalman filter position fix measurement, inwhich case the [k, k+1] interval starts and ends at the same time, or asuccession of measurements, in which case the interval [k, k+1] startsand ends at different times. The survey interval [k, k+1] in DR Function90 and SEC Function 130FIG. 5 extends from the start of interval [k,k+1] at sample “k” to the end of the [k, k+1] interval at sample “k+1”.Likewise, the survey interval [k+1, k+2] in the DR Function 110 and SECFunction 150 in FIG. 5 extends from the start of interval [k+1, k+2] tothe end of interval [k+1, k+2]. The survey intervals [k, k+1] and [k+1,k+2] will overlap at the end of the [k, k+1] interval.

Therefore, FIG. 5 shows two parallel DR and SEC function boxes toindicate the possible concurrent execution of two DR and SEC functionsfor survey intervals [k, k+1] and [k+1, k+2]. Each pair of processes, aDR process followed by a respective SEC process, is therefore a genericprocess, each pair being started by a host process for a given surveyinterval and then terminated when their operation is ended.

In the alternative, each pair could be the functional object of ageneric class that is initialized and executed for the survey interval[k, k+1] or [k+1, k+2] assigned to them, and then re-initialize for thenext survey interval [k+3, k+4] or [k+4, k+5] assigned to them.

The DR Function

FIG. 6 shows the DR function for the survey interval [k, k+1]. Thesub-routine of FIG. 6 begins when the sub-routine exits block 60 viasignal path 86 on FIG. 5 and enters FIG. 6 at START block 92 after whichit advances to HAS INTERVAL [k, k+1] STARTED, decision box 94. Ifdecision box 94 determines that the traverse for interval [k, k+1] hasstarted, the routine exits decision box 94 via YES path 96 to the HASINTERVAL [k, k+1] ENDED decision box 98. If the routine determines thatthe survey interval [k, k+1] has not ended, exits via the NO path 100 tothe RECORD SMOOTHER DATA box 102. The DR Function routine then recordsthe time-present position values to a smoother data file in a set ofsmoother data files that it open on first pass through box 102. Theroutine continues to record smoother values exiting box 102 to the DONEbox 103 on each subsequent pass until the HAS INTERVAL [k, k+1] ENDEDdecision box 98 has determined that [k, k+1] has ended. On determiningthat interval [k, k+1] has ended, the routine exits decision box 98 viathe YES path 104 to the CLOSE SMOOTHER DATA FILE box 106 at which timethe routine closes the smoother files in the allocated memory. Each timethe routine completes the task of blocks 102 or 106, the routine passesvia paths 107 or 108 respectively to the DONE block 103, after which itfollows path 132 in FIG. 5 to the RUN THE SEC FUNCTION FOR SURVEYINTERVAL [k, k+1] (FIG. 7) block 130. FIG. 7 shows the steps in the SECroutine of block 130. The routine is entered via signal path 132 tostart block 131. Thereafter the DR function of block 90 for the surveyinterval [k, k+1] ceases to be active.

The DR function thus records smoother values from the start to the endof interval [k, k+1]. This set of smoother files is then applicable tothe survey interval [k, k+1]. Each successive DR function generates aset of smoother files for each successive survey interval.

Typically survey intervals are defined between sequential start and endposition fixes (i.e., one after the other), but can be defined toinclude other position fixes between them. The DR function generatesfiles of values to be reprocessed, containing the navigation values tobe corrected and the AINS Kalman filter values required by the smootheralgorithm. The DR function generates one file or set of files for eachsurvey interval to be reprocessed.

As the operator enables reprocessing, the DR function writes the valuesrequired by the smoother to a smoother data file or set of files on themass storage memory 46 beginning at a starting position fix interval PF1and ending at an end position fix interval PF2 for a given surveyinterval. The DR function determines the time to start and stoprecording when the operator directs the AINS-LSSRP to enter positions atPF1 and PF2 via the input/output interface device 48. At PF1, the DRfunction opens the smoother data file(s) and begins recording subject tothe AINS-LSSRP confirming that it is at rest. Data continues to berecorded as the AINS-LSSRP moves to the next position fix at PF2 wherethe operator brings the AINS-LSSRP to rest and provides a PF2 signal.The DR function closes the smoother data file(s) when the AINS-LSSRPbegins to move again. The SEC function then runs the smoother on therecorded values and computes smoothed navigation solutions. Thenavigation solutions can be for the stake or control positions, or for atimed series of values during the survey segment.

As the AINS-LSSRP continues to move, the DR function continues to writevalues required by the MBFS to the next smoother data file on the massstorage memory 46 beginning at a starting position fix PF1 and ending atan end position fix PF2. The DR function determines the time to startand stop recording when the operator directs the AINS-LSSRP to enterpositions at PF1 and PF2 via the interface device 48. As before, at theend of the PF2 interval, the DR function closes smoother values file.

The SEC Function

FIG. 7 shows the SEC function for the survey interval [k, k+1]. Thesub-routine of FIG. 7 begins on FIG. 5 or FIG. 6 when the sub-routineexits block 90 via signal path 132 and enters FIG. 7 at START block 131after which it advances to the HAS INTERVAL [k, k+1] ENDED ? decisionbox 134. The test for this determination can involve a manual signalfrom the surveyor or an evaluation of velocity or position signals todetermine if the package has again started moving. The SEC Function forthe survey interval [k, k+1] will run concurrently with the DR Functionfor the survey interval [k+1, k+2]. The exceptions are the first andlast position fixes in a survey job. The SEC Function tests for the endof an interval [k, k+1] during which position fixes are processed. Ifthe decision box 134 determines that the interval [k, k+1] is not ended,i.e., the DR function continues to record time-indexed position valuesas the traverse continues, and the SEC Function routine advances via NOpath 135 to the DONE box 146 and then via signal path 148 to ENTER box52 on FIG. 5.

If the decision box 134 determines that the [k, k+1] interval is ended,the SEC Function routine advances via YES path 136 to the HAS THE DRFUNCTION FINISHED RECORDING AND CLOSED DATA FILE FOR INTERVAL [k, k+1]?decision block 138 to determine if the DR Function has recorded acomplete set of smoother values for the survey interval [k, k+1].

If the data set is not complete, the SEC Function routine advances viathe NO path 139 to the DONE box 146, exiting the DONE box via signalpath 148 to FIG. 5 to ENTER box 52 for another iteration.

If the data set exists and is complete, the SEC Function exits decisionbox 138 via the YES signal path 140 to the RUN SMOOTHER AND CORRECTPOSITION SOLUTIONS box 142. Box 142 functions to launch the smoother,which processes the data set and computes a set of smoothed navigationsolutions for the [k, k+1] survey interval. The smoothing and errorcorrection (SEC) function of box 142 run a smoothing algorithm, such asthe MBFS of equations 12-17 on the smoother data file to computesmoothed estimates of position error in the real-time positionsolutions. The smoother then corrects the real-time position solutionsto obtain smoothed position solutions with better accuracy than thereal-time position solutions.

The smoothed navigation solution has the best achievable accuracy withthe values recorded during the survey interval, and hence is called thebest estimate of trajectory (BET). When the smoother has completedprocessing the smoother values, the SEC Function routine for the surveyinterval [k, k+1] exits via signal path 144 to the DONE box 146. Theroutine exits the DONE box via signal path 148 to FIG. 5 to ENTER box 52for another iteration. On exiting box 146, the SEC Function for thetraverse of interval [k, k+1] increments the index counter for the nexttraverse and the [k+1, k+2] interval. After exiting block 130, the SECfunction for interval [k, k+1] ceases to be active.

As the SEC Function routine completes the SEC computation of thetime-indexed position value data stored during the traverse of interval[k, k+1], all files required by the SEC for this survey interval can bedeleted to limit the growth of data storage space. In principal, thisfunction is not required if data storage space is unconstrained orotherwise not an issue.

On the next pass, the subroutine operates the same performing the samesteps on FIG. 5 from box 52 through box 60. As a result of the indexcounters being incremented from “k” to “k+1” and “k+1” to “k+2”, thenext traverse leaves block 60 via path 88 and starts the next traversewith the RUN THE DR FUNCTION FOR SURVEY INTERVAL [k+1, k+2] (FIG. 6),box 110. The jump to box 110 marks the start of the next or subsequentpair of DR, SEC Functions. The functions of block 110, path 152 andblock 150 are identical in operation to those of blocks 90, path 132 andblock 130 discussed above. The routine then operates through the nexttraverse and again increments the PF index registers.

The SEC function can operate concurrently with the DR function toprocess the file or set of files most recently generated by the DRfunction. The SEC function will for example reprocess the values fromthe last survey interval files while the DR function records valuesduring the current survey interval.

While the invention has been explained in connection with severalembodiments, it is intended that the appended claims be used to limitthe scope of this patent.

What is claimed is:
 1. A Land Surveyor System with Reprocessing (LSSRP)comprising: an AINS providing a sequence of time-indexed presentposition values in response to the LSSRP being moved from a first knownposition value at the start of a survey interval to a second knownposition value at the end of the survey interval, a Position ComputingSystem (PCS) coupled to receive and store the sequence of time-indexedpresent position values as a surveyor carries the LSSRP from the firstknown position to the second known position, the PCS and the AINS beingintegrally coupled into a package to be carried by a surveyor, thepackage further comprising an input/output interface device having ameans for inputting and time-indexing successive first and second knownpresent position values at respective successive known present positionfixes, each successive pair of known present position valuesestablishing the beginning and end of a survey interval, the PCS havinga reprocessing computer and program means coupled to receive and storethe successive time-indexed known present position fix values and forprocessing the indexed present position values with a smoothingalgorithm to provide indexed and adjusted present position values for atleast some of the indexed present position values between the firstknown position fix value at the start of the survey interval and thesecond known position fix value at the end of the survey interval, thePCS also having, a switch means for signaling the AINS and the Kalmanfilter that the unit is stationary by use of an algorithm, running inthe PCS reprocessing computer and program means, for deducing zerovelocity from computed inertial velocity.
 2. The LSSRP of claim 1wherein the AINS uses a Kalman filter responsive to at least two sourcesof aiding signals, the PCS having an aiding signal selector algorithmcharacterized to select the most accurate aiding signal for use by theKalman filter from all available aiding signals.
 3. The LSSRP of claim 1wherein the reprocessing computer and program means smoothing algorithmis a Modified Bryson-Frazier smoother (MBFS).
 4. The LSSRP of claim 1wherein the reprocessing computer and program means smoothing algorithmis a modified Bryson-Frazier smoother (MBFS) mechanized using thefollowing equations and definitions for steps and definitions: dataavailable to the MBFS at iteration k from the AINS-LSSRP Kalman filter:Φ(k; k−1) transition matrix from iteration k−1 to iteration k, H_(k)measurement matrix, K_(k) Kalman gain, S_(k) Kalman innovationscovariance, {overscore (ξ)}_(k) innovations vector,{overscore({circumflex over (x)})}_(k) ⁻, {overscore({circumflex over(x)})}_(k) ⁺ Kalman estimated error state, P_(k) ⁻, P_(k) ⁺ Kalmangenerated estimation error VCV matrix, and where, the backwardsextrapolation follows: {overscore (λ)}_(k−1) ⁺=Φ^(T)(k:k−1){overscore(λ)}_(k) ⁻,  (12) Λ_(k−1) ⁺=Φ^(T)(k:k−1)Λ_(k) ⁻Φ(k:k−1),  (13) and theadjoint measurement update follows: {overscore (λ)}_(k) ⁻=(I−H _(k) K_(k)){overscore (λ)}_(k) ⁺ −H _(k) S _(k) ⁻¹{overscore (ξ)}_(k),  (14)Λ_(k) ⁻=(I−H _(k) K _(k))^(T)Λ_(k) ⁺(I−H _(k) K _(k))+H _(k) ^(T) S _(k)H _(k),  (15) and where: {overscore (λ)}_(k) ⁻ is the a priori adjointstate vector, Λ_(k) ⁻ is the a priori adjoint VCV matrix, {overscore(λ)}_(k) ⁺ is the a posteriori state vector, and {overscore (λ)}_(k) ⁺is the a posteriori adjoint VCV matrix; and where: the smoothed stateand estimation error VCV matrix is defined by: {overscore (x)} _(k) ^(s)={overscore (x)} _(k) ⁻ −P _(k) ⁻{overscore (λ)}_(k) ⁻ ={overscore (x)}_(k) ⁺ −P _(k) ⁺{overscore (λ)}_(k) ⁺,  (16) P _(k) ^(s) =P _(k) ⁻(I−Λ_(k) ⁻ P _(k) ⁻)=P _(k) ⁺(I−Λ _(k) ⁺ P _(k) ⁺),  (17) and where thesmoothed state vector is defined by: $\begin{matrix}{{\overset{\_}{x}}_{k}^{s} = \begin{bmatrix}{\delta \quad {\overset{\_}{r}}_{s}} \\{\overset{\_}{x}}_{remaining}^{s}\end{bmatrix}} & (19)\end{matrix}$

where δ{overscore (r)}_(s) is the smoothed estimate of AINS positionerror and {overscore (x)}_(remaining) ^(s) is the sub-vector of smoothederror states other than δ{overscore (r)}_(s) and where the AINS positionvector {overscore (r)}_(s) _(k) ^(e) is obtained from the errorcorrection difference matrix (20) using earth fixed Cartesiancoordinates (X, Y, Z components) as $\begin{matrix}{{\overset{\_}{r}}_{s_{k}}^{e} = {{{\overset{\_}{r}}_{k}^{e} - {\delta \quad {\overset{\_}{r}}_{s}}} = {\begin{bmatrix}{{\hat{r}}_{x}^{e} - {\delta \quad {\hat{r}}_{s_{x}}^{e}}} \\{{\hat{r}}_{y}^{e} - {\delta \quad {\hat{r}}_{s_{y}}^{e}}} \\{{\hat{r}}_{z}^{e} - {\delta \quad {\hat{r}}_{s_{z}}^{e}}}\end{bmatrix}.}}} & (20)\end{matrix}$


5. The LSSRP of claim 1 wherein the input/output interface device havinga means for inputting and time-indexing successive known presentposition values further comprises: a computer key pad and a read-outdisplay electrically coupled to the PCS for inputting successive knownpresent position values and for signaling the start of reprocessingafter inputting each successive known present position value.
 6. TheLSSRP of claim 1 wherein the PCS coupled to receive and store thesequence of time-indexed present position values further comprises: amass storage memory for storing the sequence of time-indexed presentposition values.
 7. The LSSRP of claim 6 wherein the mass storage memoryfor storing the sequence of time-indexed present position values islinked to the reprocessing computer and program mean by a radio link. 8.The LSSRP of claim 1 wherein the switch means is a manually operatedswitch with which the surveyor manually signals the AINS that the unitis stationary.
 9. The LSSRP of claim 1 wherein the switch meanscomprises a mechanical closure coupled to the package and electricallycoupled to the AINS to signal the AINS that the unit is stationary, themechanical closure being transferred by operation of a lever or plungercontacting the ground.
 10. A Land Surveyor System with Reprocessing(LSSRP) transported by a surveyor moving from a first known position atthe start of a survey interval to a second known position at the end ofthe survey interval, the LSSRP comprising: an Aided Inertial NavigationSystem (AINS) having a Kalman filter coupled to be responsive to atleast a first source of aiding time-indexed values, the AINS providing acontinuing sequence of time-indexed present position values, a PositionComputing System (PCS) having a program for storing the continuingsequence of time-indexed present position values in a memory and foroutputting the time-indexed present position value of the PCS as thesurveyor moves from the first known position to the second knownposition, the surveyor using the output time-indexed present positionvalue to locate at least one predetermined stake position, the PCSfurther comprising a reprocessing computer and program means activatedat the second known position to access and process the stored continuingsequence of time-indexed present position values with an optimalsmoothing program to provide indexed and adjusted present positionvalues for at least some of the continuing sequence of time-indexedpresent position values, and wherein, the PCS and the AINS areintegrally coupled into a package to be carried by and used by asurveyor, the package further comprising an input/output interfacedevice having a means for inputting and time-indexing successive knownpresent position values at respective successive known present positionfixes, each successive pair of known present position valuesestablishing the beginning and end of a survey interval, the PCS alsohaving a switch means for signaling the AINS that the package isstationary.
 11. The LSSRP of claim 10 wherein the PCS further comprisesan aiding signal selector for analyzing the aiding position signalsavailable to the AINS and for commanding the AINS to select and use thehighest accuracy aiding position signal available.
 12. The LSSRP ofclaim 11 wherein the aiding signal selector for analyzing the aidingposition signals available to the AINS monitors for loss of differentialGPS and in the event differential GPS is lost, the aiding signalselector directs the AINS to not use GPS signals as aiding positionsignals until differential GPS is restored.
 13. The LSSRP of claim 11wherein the aiding signal selector is further characterized to receiveall aiding position signals and to select and provide the highestaccuracy aiding position signal to the AINS for use as an input to theKalman filter.
 14. The LSSRP of claim 10 wherein the PCS furthercomprises: a mass storage memory for storing the sequence oftime-indexed present position values in an array of memory locations forlater recall.
 15. The LSSRP of claim 10 wherein the PCS and AINS packagefurther comprises a switch means with which the surveyor manuallysignals the AINS that the unit is stationary.
 16. The LSSRP of claim 15wherein the switch means is further characterized to be coupled to thepackage and electrically coupled to the AINS and to automatically signalthe start of a ZUPD on contact with the ground.
 17. A Land SurveyorSystem with Reprocessing (LSSRP) to be carried or transported by asurveyor along a predetermined path or a zigzag pattern of parallelseismic lines to locate and record the position fixes of stakes that thesurveyor positions in accordance with a pre-planned grid ofpredetermined locations comprising: an AINS programmed to provide asequence of time-indexed present position values in response to theLSSRP being moved from a first known position fix location or “tie-down”at the start of a survey interval to a second known position fixlocation or “tie-down” at the end of the survey interval, a PositionComputing System (PCS) coupled to the AINS to receive and store thesequence of time-indexed present position values from the AINS as thesurveyor moves the Land Surveyor System with Reprocessing (LSSRP) fromthe first known position fix location to the second known position fixlocation, the PCS and the AINS being integrally coupled into a packageto be carried by a surveyor, the package further comprising: aninput/output interface device having a means for inputting successiveknown present position fix location values at respective successiveknown present position fix locations, each successive pair of knownpresent position values establishing the beginning and the end of asurvey interval, a reprocessing computer running a reprocessing programto process the indexed present position values with a smoothingalgorithm, the reprocessing computer and smoothing algorithm calculatingand storing smoothed and corrected indexed and adjusted present positionvalues at the end of each survey interval, the resulting smoothed andcorrected indexed and adjusted present position values being used tocorrect the position value or fix location of at least one stakepositioned between the first known position fix, location at the startof the survey interval and the second known position fix location at theend of the survey interval, the package having a switch means coupled tothe package and electrically coupled to the PCS to signal that thepackage is stationary, the PCS being coupled to receive and provide atleast two sources of aiding signals to a Kalman filter, at least onesource being a radio linked differentially corrected GPS signal, and asignal selector or program for automatically selecting the most accurateaiding signal for use by the Kalman filter from all available aidingsignals.
 18. The Surveyor System with Reprocessing (LSSRP) of claim 17wherein the switch means further comprises a mechanical closure that iscoupled to the package and is electrically coupled to the AINS to signalthat the package is stationary, the mechanical closure being transferredby operation of a lever or plunger contacting the ground.
 19. TheSurveyor System with Reprocessing (LSSRP) of claim 17 wherein the switchmeans comprises an algorithm running in the AINS and or the PCS forautomatically signaling when the package is stationary.